A child can count on from ten times to get , or count back ten times to get . Why does a whole ten never need all that counting, and why does only one digit change?

Grade 1 · 1.NBT.C.4 · 1.NBT.C.5

Ten more and ten less

A child can count on from 36 ten times to get 46, or count back ten times to get 26. Why does a whole ten never need all that counting, and why does only one digit change?

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Counting on and counting backKindergarten Tens and onesGrade 1

Unlocks

Adding on an open number lineGrade 2 Subtracting multiples of tenGrade 1

Where you are 7 in Adding and subtracting within 20

Number9

Arithmetic5

Addition and subtraction12

Adding and subtracting within 207

▴ 1 above Doubles and near doubles Subtracting within ten

Ten more and ten less

Counting on to add and counting back to subtract Making ten and bridging through ten ▾ Show all 7 (1 more)

When you reach for it

Ask a child for 4 + 10 and many will hold up four fingers and count on, “five, six, seven...”, all the way to fourteen. That works, but it takes ten careful counts, and a single slip gives 13 or 15. There is a much shorter way, and it is worth teaching on purpose because it is one of the first places a child puts to work what our way of writing numbers is built on: groups of ten.

The shortcut rests on one fact from Tens and ones, where teen numbers are first seen as ten and some more. A number such as 14 is one ten and 4 ones; 36 is 3 tens and 6 ones. Adding ten adds one whole ten and no loose ones. So the loose ones stay exactly as they were, and the count of tens goes up by one. Written in digits, the ones digit does not change and the tens digit goes up by one: 36 + 10 = 46. Taking ten away is the same thing backwards: 46 - 10 = 36. (The one surprise, a tens digit of 9, is Example 10.) The child does not need to count ten times. They only need to ask “how many tens now?”

This lesson covers four situations, in the order a child meets them:

ten added to a number from 0 to 9, as 10 + 4 or 4 + 10, which makes a teen number;
ten added to a teen number or any larger two-digit number, as 13 + 10 or 36 + 10;
ten more and ten less than any number, the two moves side by side, and how they sit next to one more and one less;
counting on or back by tens from a number that does not end in 0, as 7, 17, 27, 37.

The pictures are Ten frames, two rows of five boxes filled along the top row first, with dark and light counters as in the number-bond lessons. A full frame is one ten you can see at a glance. The other picture is the hundred chart, the numbers 1 to 100 in rows of ten.

The procedure

The lesson has three parts: adding ten, then ten more and ten less as a pair, then counting by tens from any number, which is the same move made again and again.

Adding ten

Ten and a few more. Put out a full ten frame and 4 more counters in a second frame, as in Example 1. There are ten in the full frame and four more, so 10 + 4 = 14. Nothing needs counting except the four. This is exactly what the number 14 means: the 1 stands for one ten and the 4 for four ones. The same goes for every number from 0 to 9: 10 + 1 = 11, 10 + 7 = 17, 10 + 9 = 19, and 10 + 0 = 10.

An adult reading 14 sees the ten first. A child hearing “fourteen” hears the four first, and “eleven” and “twelve” do not say the ten at all. That mismatch is why a child who can count to twenty may still not see that 10 + 4 is 14 without counting. Saying it both ways helps: “ten and four is fourteen”, and “fourteen is ten and four”.

The ten second. For 4 + 10 the child sees the small number first and wants to count on ten times. Counting on from the larger number, as in Counting on to add and counting back to subtract, helps, but here there is something better still. Four counters and a full frame are the same counters as a full frame and four counters: sliding the two groups past each other does not change how many there are (see Addition as putting together). So 4 + 10 is also 14, and the child can think of it as “ten and four”.

Ten more than a teen or a two-digit number. Show 36 as three full frames and a frame with 6 counters. Adding ten means bringing one more full frame.

Figure 1Ten more than 36 is one more full frame. The 6 loose counters do not move.

The new frame joins the other full frames. The frame with 6 counters is not touched, so there are still 6 loose counters and now 4 full frames: 46. In words, “three tens and six, and one more ten, is four tens and six”. The number name changes the same way: thirty-six becomes forty-six. The same thinking gives 13 + 10 = 23 (one ten becomes two tens, the 3 stays) and 40 + 10 = 50 (four tens become five tens, and there were no loose ones to begin with).

A hundred chart shows the same fact from a different side. Each row of the chart holds ten numbers, so moving from any square to the square directly below it moves ten further along.

Figure 2Each row holds ten numbers, so ten more is the square just below and ten less is the square just above.

Below 36 sits 46, and above it sits 26. Every column keeps the same ones digit all the way down, and each row down has one more ten. A child who notices that has found the pattern for themselves.

Ten more and ten less

Ten less. Taking ten away is the same move backwards: one full frame goes, and the loose counters stay. Take a full frame away from the picture of 46 and it becomes 36 again, so 46 - 10 = 36. For a teen number, taking away its one full frame leaves just the loose counters: 17 - 10 = 7. Each of these is also the addition read the other way, part of a fact family: 36 + 10 = 46 and 46 - 10 = 36 use the same three numbers.

One pair of numbers, said from either end. Ten more than 36 is 46, and ten less than 46 is 36: one fact, read from opposite ends. It can also be said with the bigger number first: 46 is ten more than 36, and 36 is ten less than 46. It is worth saying all four sentences aloud with the child, because a question can come in any of these shapes. A question such as “which number is 56 ten more than?” gives the bigger number and asks for the smaller, so it is answered by going ten less: 46. Example 7 works through both kinds.

Ten beside one. The child already knows one more and one less: the number just after and just before. Put the two moves side by side and the place-value story shows clearly. One more adds a single loose one, so it changes the ones digit: 45 becomes 46. Ten more adds a whole ten, so it changes the tens digit: 45 becomes 55. On the hundred chart the two moves go in different directions.

Figure 3Around 45. One more and one less sit beside it; ten more and ten less sit below and above it.

One more is a step to the right along the row and one less a step to the left. Ten more is a step down the column and ten less a step up. Because each move touches only its own digit, the moves can be mixed freely, as in Example 9: +10 changes the tens, -1 changes the ones, and neither disturbs the other. (The exceptions are when a digit would run past 9 or below 0, as in 49 + 1 = 50 or 95 + 10 = 105; the Boundaries say more.)

The same move for bigger numbers. Nothing changes when there are hundreds too. In 245 there are 2 hundreds, 4 tens and 5 ones. Ten more adds one ten, so it is 2 hundreds, 5 tens and 5 ones: 245 + 10 = 255. Ten less takes one ten away: 245 - 10 = 235. Only the tens digit moves, except in two cases: ten more when the tens are already full, which is Example 10, and ten less when there are no tens at all, which is Example 8.

Counting by tens from any number

Counting by tens from 0, “ten, twenty, thirty”, is Counting by tens to one hundred. Counting by tens from any number means starting somewhere else, such as 37, and saying ten more each time:

37,\; 47,\; 57,\; 67,\; 77

Each count is the move from the last part made again. The 7 ones never change, and the tens go up by one every time. Out loud, the decade word changes and the “seven” repeats: thirty-seven, forty-seven, fifty-seven. A child who hears that rhythm has the pattern.

Figure 4Counting by tens from 37. Every hop is ten more, and every number landed on ends in 7.

On the hundred chart the same count walks straight down one column, the column of numbers ending in 7 (Figure 2 shows the column for 6). Counting back by tens walks up the column, one ten less each time: 77, 67, 57, 47, 37, 27, 17, 7. It stops at 7, because 7 has no ten left to take away.

The ones digit says where the count can land. Starting from 37, every number said ends in 7. So the count passes 57 and 67 but never lands on 55 or 60. Two numbers can be joined by jumps of ten only when they have the same ones digit.

Counting the jumps. From 37 to 77 the tens digit goes from 3 to 7, so there are 7 - 3 = 4 jumps, and four jumps of ten is forty altogether: 37 + 40 = 77. Counting by tens from a number is how a child adds 20, 30 or 40 in their head, a little before they meet it as adding two-digit numbers. Example 12 counts jumps. Reading the jumps off the tens digit only works while the count stays below the next hundred; a count that passes a hundred, as in Example 13, is easier to count jump by jump.

Past a hundred. When the count reaches a tens digit of 9, the next jump makes ten tens, which is a new hundred: 97 is followed by 107, and 498 by 508. The ones digit still holds, and the tens digit starts again from 0. Examples 10 and 13 cross a hundred this way.

Worked examples

Read each problem aloud. Ten frames drawn on paper, with buttons or counters, let the child build every one of them, and a hundred chart on the table lets them check. Once a child can say the answers without building them, they are adding ten in their head, which is the point.

Example 1

A full frame and four more

How many counters are there?

Figure 5One full ten and four more is fourteen.

Solution

The first frame is full, so it holds ten. The second frame has 4 counters. Ten and four is fourteen:

10 + 4 = 14

The child does not need to count the full frame, because a full frame is always ten. Ask them to count the whole lot once, “one, two, three...”, to see that the count agrees. After a few frames like this, they stop counting the full one.

Example 2

Six shells and ten more

Sam has 6 shells. He finds 10 more shells. How many shells does he have now?

Solution

Sam starts with 6 and adds 10, which is 6 + 10. Counting on ten times from 6 would work, but the frames give a shorter way. Put 6 counters in one frame and ten in another, then swap the two frames.

Figure 6Swapping the two frames does not change how many counters there are.

The counters are the same, so the total is the same: 6 + 10 is the same as 10 + 6, and ten and six is sixteen. Sam has 16 shells:

6 + 10 = 16

Example 3

Cars in a line

There are 13 cars in a line. 10 more cars join the line. How many cars are in the line now?

Solution

13 is one ten and 3 more. The 10 new cars are one more ten. So now there are two tens and 3 more, which is twenty-three:

13 + 10 = 23

In frames: one full frame and 3 counters, then a second full frame. The 3 loose counters never move, which is why the 3 in 13 is still there in 23. Here the child meets a number past twenty for the first time in this lesson, and the frames make it no harder than a teen.

Example 4

Ten more than thirty-six

What number is ten more than 36?

Solution

36 is three tens and 6. Ten more is one more ten, so it is four tens and 6, which is forty-six:

36 + 10 = 46

Figure 1 shows it: the 6 loose counters stay, and the full frames go from three to four. On the hundred chart in Figure 2, 46 is the square directly under 36. The two pictures are different but they say the same thing, and it is worth checking one against the other with the child.

Example 5

Beads to a friend

Zara has 47 beads. She gives 10 beads to her friend. How many beads does Zara have now?

Solution

47 is four tens and 7. Giving away 10 takes away one whole ten. That leaves three tens and 7, which is thirty-seven. Zara has 37 beads:

47 - 10 = 37

Check it with addition: if her friend gives the 10 beads back, 37 + 10 = 47, which is where Zara started. On the hundred chart, 37 is the square just above 47.

The same thinking works for a teen number. Ten less than 18 takes away its one ten and leaves the 8: 18 - 10 = 8.

Example 6

All around forty-five

What are one more, one less, ten more and ten less than 45?

Solution

45 is four tens and 5 ones. Take the four moves one at a time.

One more adds a single one: four tens and 6, so one more than 45 is 46.
One less takes a single one away: four tens and 4, so one less than 45 is 44.
Ten more adds a whole ten: five tens and 5, so ten more than 45 is 55.
Ten less takes a whole ten away: three tens and 5, so ten less than 45 is 35.

As sums: 45 + 1 = 46, 45 - 1 = 44, 45 + 10 = 55 and 45 - 10 = 35. Figure 3 shows the four answers as the squares around 45 on the hundred chart.

Look at the digits. In 46 and 44 the tens digit is still 4; only the ones moved. In 55 and 35 the ones digit is still 5; only the tens moved. Asking the child “which digit changed, and why that one?” is the whole lesson in one question.

Example 7

Ten more than what?

Fill in each box.

56 is ten more than \square.
Ten less than \square is 29.

Solution

The first sentence says that \square + 10 = 56. The box is the smaller number, and 56 is ten bigger, so the box is ten less than 56. Five tens and 6, less one ten, is four tens and 6:

56 - 10 = 46

Check: 46 + 10 = 56, so 56 really is ten more than 46.

The second sentence says that \square - 10 = 29. Now the box is the bigger number, so it is ten more than 29. Two tens and 9, and one more ten, is three tens and 9:

29 + 10 = 39

Check: 39 - 10 = 29. A question worded with “more” can need ten less, and one worded with “less” can need ten more. The child should ask which number is the bigger one, not which word the question uses.

Example 8

Ten less when there are no tens

What number is ten more than 205? What number is ten less than 205?

Solution

205 is 2 hundreds, 0 tens and 5 ones. Ten more brings one ten, so there is now 1 ten: 2 hundreds, 1 ten and 5 ones, which is 215:

205 + 10 = 215

Ten less is harder, because there are no tens to take away. The tens are all bundled up inside the hundreds. So open one hundred into ten tens. That leaves 1 hundred, 10 tens and 5 ones, which is still the same amount, because one hundred is ten tens. Now one ten can go, leaving 1 hundred, 9 tens and 5 ones, which is one hundred and ninety-five:

205 - 10 = 195

Check: 195 + 10 makes the 9 tens into ten tens, which bundle back into a hundred, and gives 205. Here two digits changed, the hundreds and the tens, because a hundred had to be opened. That opening up is the start of Regrouping in subtraction. The ones digit, 5, still did not move.

Example 9

Ones moves and tens moves

Start at 58. Add ten, add ten again, take one away, then take ten away. Where do you finish?

Solution

Make each move in turn. Each one touches only its own digit.

Add ten: the tens go up, 58 + 10 = 68.
Add ten again: 68 + 10 = 78.
Take one away: now the ones go down, 78 - 1 = 77.
Take ten away: the tens go down, 77 - 10 = 67.

The finish is 67. There is a second way to see it. Altogether the tens went up twice and down once, so they went up by one ten; the ones went down by one. Five tens and 8 becomes six tens and 7, which is 67 again. On a hundred chart this is a little walk: down, down, left, up.

Example 10

The frog on the number track

A frog sits on 7. Each jump takes it 10 squares further along. Where does it land after each jump? Where is it after 10 jumps?

Solution

Each jump adds ten, so the 7 ones never change and the tens go up by one each time:

7,\; 17,\; 27,\; 37,\; 47,\; 57,\; 67,\; 77,\; 87,\; 97,\; 107

Most of the way this is the familiar move: 47 + 10 = 57, 87 + 10 = 97. The last jump is the interesting one. At 97 there are 9 tens and 7 ones. One more ten makes ten tens, and ten tens is one hundred. So after 10 jumps the frog is on 107, which is one hundred and 7:

97 + 10 = 107

Here the tens digit does not just go up by one, because there is no digit after 9. The ten tens are bundled into a hundred, the tens digit becomes 0, and a hundreds digit appears. Ten jumps of ten also took the frog exactly 100 squares, from 7 to 107.

Jumping back is the mirror. In 107 the tens digit is 0, so to take a ten away the hundred is opened up into ten tens; one ten goes, and nine tens and 7 are left: 107 - 10 = 97. The frog has been counting by tens from 7, and every number it lands on ends in 7.

Example 11

Counting back by tens

Count back by tens from 94 as far as you can go. Where must you stop, and why?

Solution

Counting back by tens means saying ten less each time. The 4 ones never change and the tens go down by one each count:

94,\; 84,\; 74,\; 64,\; 54,\; 44,\; 34,\; 24,\; 14,\; 4

The count stops at 4. Four is just 4 ones with no ten in it, so there is no whole ten left to take away; 4 - 10 has no answer while we are counting whole things. The child went back 9 times, which is 9 tens or 90 altogether, and indeed 94 - 90 = 4. On a hundred chart this is the column of numbers ending in 4, read from the bottom up.

Example 12

How many jumps?

A counter sits on 23 on a number track and moves only in jumps of ten. How many jumps take it to 73? Could it ever land on 75?

Solution

Each jump is ten more, so the 3 ones stay and the tens go up by one:

23,\; 33,\; 43,\; 53,\; 63,\; 73

That is 5 jumps. The child does not need to list them: 23 is two tens and 3, 73 is seven tens and 3, and the tens went from 2 to 7, which is 7 - 2 = 5 more tens. Five jumps of ten is fifty, so 23 + 50 = 73.

The counter can never land on 75. Every number it lands on ends in 3, because a jump of ten never touches the ones. It goes from 73 straight to 83, passing over 75. To reach 75 from 23 it would need some ones moves too.

Example 13

A jar filling by tens

A jar holds 468 beads. Each day 10 more beads are put in. After how many days does the jar first hold more than 500 beads, and how many beads is that?

Solution

Count on by tens from 468, one count for each day. The 8 ones never change.

After 1 day: 468 + 10 = 478.
After 2 days: 478 + 10 = 488.
After 3 days: 488 + 10 = 498. Not yet: 498 is still less than 500.
After 4 days: 498 + 10 = 508.

The last step is the one to slow down on. 498 is 4 hundreds, 9 tens and 8 ones. One more ten makes ten tens, which is another hundred, so it becomes 5 hundreds, 0 tens and 8 ones: 508. After 4 days the jar first holds more than 500 beads, and it holds 508.

Check: four days of ten beads is 40 beads, and 468 + 40 = 508.

Boundaries

The tens digit must be less than 9 for only one digit to change. In 36 + 10 or 245 + 10 only the tens digit moves. When the tens digit is already 9, as in 95 + 10 = 105, 90 + 10 = 100 or 296 + 10 = 306, the ten tens make a new hundred. The ones still stay put every time, which is the part that never fails.
Ten less needs a ten to take away. 17 - 10 = 7 and 10 - 10 = 0, but with 6 counters there is no ten to take: 6 - 10 has no answer while we count whole things. Every number from 10 up has at least one ten, which is why a count back by tens stops below 10.
Ten less when the tens digit is 0. In 304 - 10 every ten is bundled inside a hundred, so one hundred has to be opened up into ten tens first; then one ten goes, leaving 294. That opening up is Regrouping in subtraction.
It has to be a whole ten. Adding 10 leaves the ones alone because 10 has no ones of its own. Adding 9 or 11 changes the ones as well: 36 + 9 = 45, not 46. Those need Making ten and bridging through ten or Adding two-digit numbers without regrouping.
A count by tens only reaches numbers with the same ones digit. From 23, jumps of ten land on 33, 43, 53 and so on, never on 75. Reaching a number with a different ones digit needs ones moves as well.
One more is a step to the right only inside a row. On the hundred chart, one step right is one more only while the row lasts. One more than 50 is 51, which is at the start of the next row, not beside 50. Ten more is always the square straight below, from 1 to 90.
The ten can come first or second. 4 + 10 and 10 + 4 are both 14 only because the order of adding two numbers does not change the total.

Where this goes next

Ten more and ten less are the steps a child uses to find their way around every number up to a hundred and past it, and counting by tens from any start, 7, 17, 27, is the same step repeated. Counting by tens from 0 is Counting by tens to one hundred, and the same lesson counts by hundreds.

The same move works for more than one ten at once. 34 + 20 adds two tens and leaves the 4 alone, which is where Adding two-digit numbers without regrouping begins. It also sits inside Making ten and bridging through ten: 9 + 5 becomes 10 + 4, and this lesson is why 10 + 4 is then easy. With hundreds, adding 100 is the same move one place over: the hundreds go up by one and the tens and ones stay, the next step in Adding three-digit numbers and in Reading and writing numbers to 1,000. On an open number line, a jump of ten is the same move drawn as a hop, exactly as in Figure 4.

Exercises

Ten and some more

10 + 5 = \square
8 + 10 = \square
10 + \square = 17
\square + 10 = 12

Pictures

Figure 7Frames for Exercises 5 to 7.

How many counters are in stack A? How many will there be if you add one more full frame?
How many counters are in stack B? How many will there be if you add one more full frame?
How many counters are in stack C? How many will there be if you add one more full frame?

Ten more and ten less

What number is ten more than 23?
What number is ten more than 58?
64 - 10 = \square
What number is ten less than 19?
40 + 10 = \square
There are 52 children on a bus. 10 more children get on. How many children are on the bus now?
What number is ten more than 426? What number is ten less than 426?
What are one more, one less, ten more and ten less than 62?
74 is ten more than \square.
Ten less than \square is 39.
What number is ten more than 503? What number is ten less than 503?

A piece of the chart

Figure 8A piece of a hundred chart, for Exercise 19.

Which numbers go in the squares marked A, B, C, D and E?

Counting by tens

Count on by tens from 4 to 64.
Count back by tens from 86 as far as you can go.
Fill in the boxes: 39, 49, 59, \square, \square, \square
Fill in the boxes: 72, 62, \square, \square, 32
Does each count go up by one, down by one, up by ten or down by ten? (a) 28, 38, 48, 58; (b) 61, 60, 59, 58; (c) 95, 85, 75, 65; (d) 103, 104, 105, 106.
How many jumps of ten take you from 16 to 76?
Count on by tens from 275 to 335.
Lena has 8 stickers. Every week she is given a pack of 10 more. How many stickers does she have after 5 weeks?

Explain

Mia says 3 + 10 and 10 + 3 give different answers, because the 10 comes first in one of them. Is she right? Show it with counters.
When you add ten to 34, why does the 4 stay the same?
What number is ten more than 95? Why does the answer have three digits?
You have 6 counters. Can you take 10 counters away? How do you know?
Ravi counts by tens, starting at 23. Will he say 83? Will he say 85? How do you know?
On a hundred chart, why is ten more than a number the square just below it, while one more, inside a row, is the square just to its right?
Ten less than 108 is 98. Why does the answer have only two digits?

Answers

15. One full ten and 5 more is fifteen: 10 + 5 = 15.
18. Swap them: 8 + 10 is the same as 10 + 8, ten and eight, so 8 + 10 = 18.
7. 17 is one ten and 7 ones, so 10 + 7 = 17.
2. 12 is one ten and 2 ones, so 2 + 10 = 12.
17, then 27. Stack A is one full frame and 7 counters. One more full frame makes two tens and 7: 17 + 10 = 27.
25, then 35. Stack B is two full frames and 5 counters. One more full frame makes three tens and 5: 25 + 10 = 35.
41, then 51. Stack C is four full frames and 1 counter. One more full frame makes five tens and 1: 41 + 10 = 51.
33. Two tens and 3, and one more ten, is three tens and 3: 23 + 10 = 33.
68. Five tens and 8, and one more ten, is six tens and 8: 58 + 10 = 68.
54. Six tens and 4, take away one ten, leaves five tens and 4: 64 - 10 = 54.
9. 19 is one ten and 9; taking the ten away leaves 9: 19 - 10 = 9.
50. Four tens and one more ten is five tens, with no loose ones: 40 + 10 = 50.
62 children. 52 is five tens and 2; ten more makes six tens and 2: 52 + 10 = 62.
436 and 416. 426 is 4 hundreds, 2 tens and 6 ones. Ten more makes 3 tens: 426 + 10 = 436. Ten less leaves 1 ten: 426 - 10 = 416.
63, 61, 72 and 52. 62 is six tens and 2. One more and one less change the ones: 62 + 1 = 63 and 62 - 1 = 61. Ten more and ten less change the tens: 62 + 10 = 72 and 62 - 10 = 52.
64. 74 is the bigger number, so the box is ten less than 74: 74 - 10 = 64. Check: 64 + 10 = 74.
49. 39 is what is left after ten is taken away, so the box is ten more than 39: 39 + 10 = 49. Check: 49 - 10 = 39.
513 and 493. 503 is 5 hundreds, 0 tens and 3 ones. Ten more gives 1 ten: 503 + 10 = 513. For ten less, open one hundred into ten tens, making 4 hundreds, 10 tens and 3 ones; take one ten away to leave 4 hundreds, 9 tens and 3 ones: 503 - 10 = 493.
A is 48, B is 57, C is 59, D is 68 and E is 78. Up a square is ten less, 58 - 10 = 48; left is one less, 58 - 1 = 57; right is one more, 58 + 1 = 59; down is ten more, 58 + 10 = 68; and down again is ten more than that, 68 + 10 = 78.
4, 14, 24, 34, 44, 54, 64. The 4 ones stay and the tens go up by one each count.
86, 76, 66, 56, 46, 36, 26, 16, 6. The 6 ones stay and the tens go down by one each count. The count stops at 6, because 6 has no ten left to take away.
69, 79, 89. Each number is ten more than the one before: the 9 ones stay and the tens go up, 59 + 10 = 69, 69 + 10 = 79, 79 + 10 = 89.
52, 42. Each number is ten less than the one before: 62 - 10 = 52 and 52 - 10 = 42, and then 42 - 10 = 32 as printed.
(a) up by ten, (b) down by one, (c) down by ten, (d) up by one. In (a) the tens digit climbs and the 8 stays; in (b) the numbers go down one at a time, 61 - 1 = 60; in (c) the tens digit falls and the 5 stays; in (d) the ones digit climbs, 103 + 1 = 104.
6 jumps. 16 has one ten and 76 has seven tens, and 7 - 1 = 6. Six jumps of ten is sixty: 16 + 60 = 76.
275, 285, 295, 305, 315, 325, 335. The 5 ones stay. At 295 there are 9 tens, so ten more makes ten tens, a new hundred: 295 + 10 = 305.
58 stickers. Count on by tens from 8, once a week: 18, 28, 38, 48, 58. Five packs of ten is fifty, and 8 + 50 = 58.
No, they are the same. Put out 3 counters and a full frame of ten, then swap them. The counters are the same, so there are 13 either way: 3 + 10 = 13 and 10 + 3 = 13.
34 is three tens and 4 loose ones. Adding ten brings one more whole ten and no loose ones, so the 4 loose ones are not touched. Only the tens change, from three to four: 34 + 10 = 44.
105. 95 is nine tens and 5. One more ten makes ten tens, and ten tens is one hundred. So the answer is one hundred and 5: 95 + 10 = 105. It needs a third digit to show the hundred.
No. There are only 6 counters, and 6 is less than 10, so there is no full ten to take. Even taking all 6 away leaves you 4 short, because 6 + 4 = 10.
He will say 83 but not 85. Every count adds a whole ten, so the ones digit stays 3 the whole way: 23, 33, 43, 53, 63, 73, 83, which is 6 counts to reach 83. A number ending in 5 never comes up, so he goes from 83 to 93 and skips over 85.
Each row of the chart holds ten numbers. Going one square to the right moves one number along, so it is one more. Going straight down a column skips past the rest of the row and the start of the next one, ten numbers in all, so the square below is ten more. That is why every column keeps the same ones digit. At the end of a row there is no square to the right, so one more than 50, which is 51, starts the next row.
108 is 1 hundred, 0 tens and 8 ones. There is no ten to take, so the hundred is opened up into ten tens. One ten goes, leaving 9 tens and 8 ones and no hundreds at all: 98. With no hundreds left, there is nothing to write in the hundreds place, so 108 - 10 = 98 has only two digits.